Central limit theorems for functionals of stationary germ-grain models

被引：4
|
作者：
Pantle, U [1 ]
Schmidt, V [1 ]
Spodarev, E [1 ]
机构：
[1] Univ Ulm, Abt Stochast, D-89069 Ulm, Germany
来源：
ADVANCES IN APPLIED PROBABILITY | 2006年 / 38卷 / 01期
关键词：
random closed set; Boolean model; stationary random field; m-dependent random field; valuation; asymptotic normality; beta-mixing; specific intrinsic volume; Euler number;
D O I：
10.1239/aap/1143936141
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Conditions are derived for the asymptotic normality of a general class of vector-valued functionals of stationary Boolean models in the d-dimensional Euclidean space, where a Lindeberg-type central limit theorem for m-dependent random fields, m is an element of N, is applied. These functionals can be used to construct joint estimators for the vector of specific intrinsic volumes of the underlying Boolean model. Extensions to functionals of more general germ-grain models satisfying some mixing and integrability conditions are also discussed.
引用
收藏
页码：76 / 94
页数：19
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